Locally differentially private two-sample testing

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ID: 316940
2026
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Abstract
Summary We consider the problem of two-sample testing under a local differential privacy constraint where a permutation procedure is used. We develop testing procedures which are optimal up to logarithmic factors, for general discrete distributions and continuous distributions subject to a smoothness constraint. Both non-interactive and interactive tests are considered, and we show allowing interactivity results in an improvement in the minimax separation rates. Our results show that permutation procedures remain feasible in practice under local privacy constraints, despite the inability to perturb the non-private data directly and only the private views. Further, through a tighter theoretical analysis of the permutation procedure, we are able to relax a balanced sample size assumption which is imposed in the permutation testing literature regardless of the presence of the privacy constraint. Lastly, we conduct numerical experiments which demonstrate the performance of our proposed test and verify the theoretical findings, especially the improved performance enabled by allowing interactivity.
Reference Key
openalex_W4414858714 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Alexander Kent, Thomas B. Berrett, Yi Yu
Journal jurnal biometrika dan kependudukan
Year 2026
DOI
10.1093/biomet/asag034
URL
https://doi.org/10.1093/biomet/asag034
Keywords Keywords not found

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